<p>Data storage in DNA has recently emerged as a promising archival solution, offering space-efficient and long-lasting digital storage. DNA’s ultra-high density and durability make it an attractive medium for long-term data storage. Among the various approaches, combinatorial DNA encoding further enhances this potential by increasing the logical density through the use of combinations of DNA shortmers, where each sequence position is represented by a set of predefined short DNA fragments. This approach allows for the encoding of a larger data volume using fewer synthesis cycles. However, this method introduces unique challenges, particularly in terms of synthesis and sequencing errors. In this study, we focus on the characterization of errors in combinatorial DNA-based storage systems. Our analysis revealed that asymmetric combinatorial erasure errors, defined as the omission of a single shortmer from the set defining the combinatorial letter, are a prevalent error type in combinatorial DNA-based storage, particularly in large-scale systems where read coverage is limited. We analyzed two previously published datasets, observing a high frequency of erasure errors, where missing sequences obstruct the reconstruction of specific combinatorial letters. To better understand these observations, we conducted a large-scale experimental proof-of-concept of a combinatorial DNA-based storage system and evaluated the error characteristics of the system. Our analysis confirmed that erasure errors become increasingly prominent with reduced sequencing depth. We demonstrated that below 50 reads per sequence, the frequency of erasure errors sharply increased. We developed an asymmetric error-correcting code specifically designed to address these errors. The code utilizes tensor-product (TP) codes to integrate standard erasure and substitution-correcting codes (such as Reed-Solomon (RS) codes) with Varshamov-Tenengolts (VT) codes, which are asymmetric error-correcting codes. We validated the performance of our new error correction code both in simulations and in a second large-scale experiment. The experimental comparison was designed to directly compare our suggested code with the more straightforward 2D Reed-Solomon (2D RS) scheme. Our method consistently outperformed the 2D RS scheme, particularly in scenarios dominated by erasure errors. Notably, in the second large-scale experiment, our method demonstrated superior decoding accuracy even under low coverage conditions, where the traditional 2D RS approach struggled to decode the data. Our findings demonstrate the importance of tailored error correction schemes in DNA-based data storage. By directly addressing the asymmetric nature of errors in combinatorial DNA, our method provides improved decoding accuracy under a wide range of conditions. The integration of such tailored error correction methods with existing DNA-based data storage technologies has the potential to deliver more reliable and scalable DNA-based data applications.</p>